# 15-4 gyrochoron

The **15-4 gyrochoron**, also known as the **triswirl 15**, is a convex isochoric polychoron and member of the gyrochoron family with 15 paratetratruncated rhombic prisms as cells.

15-4 gyrochoron | |
---|---|

Rank | 4 |

Type | Isotopic |

Elements | |

Cells | 15 paratetratruncated rhombic prisms |

Faces | 30 isosceles triangles, 30 mirror-symmetric hexagons, 15 rectangular-symmetric hexagons |

Edges | 30+30+60 |

Vertices | 30+30 |

Vertex figure | 30+30 phyllic disphenoids |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Dual | 15-4 step prism |

Abstract & topological properties | |

Flag count | 1440 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | S_{2}(I_{2}(15)-4)×2R, order 60 |

Flag orbits | 24 |

Convex | Yes |

Nature | Tame |

Each cell of this polychoron has chiral digonal prismatic symmetry, with 2 rectangular-symmetric hexagons, 4 mirror-symmetric hexagons, and 4 isosceles triangles for faces.

Compared to other gyrochora with 15 cells, this polychoron has reflective doubled symmetry, because 15 is a factor of 4^{2}-1 = 15.

## External links edit

- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".